Kink Nucleation Research Articles

Atomic layer wear of single-crystal calcite in aqueous solution using scanning force microscopy

Scanning force microscopy (SFM) is employed to study nm-scale wear of single-crystal calcite in an aqueous solution. When the SFM tip is drawn back and forth in a linear fashion across the edge of a preexisting single atomic layer etch pit, dissolution is strongly enhanced at the point where the tip crosses the step. The wear rate as a function of contact force is consistent with a thermally activated wear process, where the activation energy is locally reduced in the strain field of the SFM tip. The activation volume for the strain dependence is on the order of the average volume per ion in the CaCO3 lattice. This study provides further support for strain enhanced nucleation of double kinks along preexisting steps.

Energy-release rate and crack kinking in anisotropic brittle solids

The energy-release rate is calculated for the inception of crack kinking in a general anisotropic solid containing a pre-existing crack. First, the stress intensity factors at the tip of an infinitesimally small kink ( K I ( k) and K II ( k) ) and the kink opening displacements (KODs) are numerically calculated by modeling the kink as continuously distributed edge dislocations. The energy-release rate, G kink, is obtained directly by calculating the work required to fully close the kink gap (KOD) and restore the required normal and shear stresses ( σ ωω and σ r ω ) that existed before kinking. This energy-release rate, G kink, is compared with that (denoted by G Irwin) obtained by applying the Irwin formula in terms of the stress intensity factors K I ( k) and K II (k) at the tip of the vanishingly small kink, for various kink angles, material properties, material symmetry orientations, and loadings. It is observed that the two methods yield exactly the same value for the rate of energy released, even though G kink corresponds to kink nucleation, whereas G Irwin to kink extension. Therefore, Irwin's formula for the energy-release rate is valid for any kink angle, material anisotropy, and loading condition (any combination of modes I and II), provided that the stress intensity factors in the formula are taken equal to those calculated at the tip of a vanishingly small kink, but not those associated with the stress components σ ωω and σ r ω prior to kinking. For different loading and material symmetry conditions, the energy-release-rate fracture criterion is compared with different stress-based fracture criteria of the fracture-path prediction.

Interplay between step velocity and morphology during the dissolution of CaCO3 surface

The interplay between the velocity and morphology of steps during the dissolution of the cleaved CaCO3(101̄4) surface in aqueous solution has been studied using atomic force microscopy (AFM). The experimental results were analyzed based on the terrace-ledge-kink model. Real-time AFM images show that, in the surface reaction regime, steps not only retreat at constant velocities which depend only on the atomic structure of the step, but also preserve a straight-edge morphology during the course of dissolution. The straight step morphology suggests that the nucleation of kinks is balanced by the annihilation of the kinks at the step during the dissolution. This result, along with the constant step velocity, can be explained in terms of a kink-kink annihilation process.

Critical-current anisotropy due to inclined and crossed linear defects.

Parallel linear defects which are inclined to the sample surface normal and crossed linear defects are introduced into ${\mathrm{DyBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals by high-energy heavy-ion irradiation. The dependence of flux penetration on temperature, fluence, and applied external magnetic field is investigated before and after irradiation. For crossed linear defects much higher pinning than for parallel defects with the same density is observed for both materials. This finding is attributed to the intersections of linear defects which allow the flux lines to be more effectively pinned than by parallel defects. In this case flux-line depinning occurs by kink-pair nucleation in the sample volume as in the Bose-glass model. From parallel linear defects the flux lines may be more easily depinned by nucleation of surface kinks. The observed low anisotropy ${\mathit{j}}_{\mathrm{\ensuremath{\parallel}}}$/${\mathit{j}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\approxeq}2 of the critical current flowing parallel or perpendicular, respectively, to the inclination plane of the defects in parallel-irradiated ${\mathrm{DyBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ is explained by different geometrical arrangment of defects and flux lines in the directions of flux-line motion. During field decrease the anisotropy is found to disappear in samples with parallel linear defects. For crossed defects the anisotropy ${\mathit{j}}_{\mathrm{\ensuremath{\parallel}}}$/${\mathit{j}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\approxeq}2 reverses in decreasing field since the flux lines are effectively pinned only in the inclination plane of the linear defects. In ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals the flux penetration is isotropic; this is understood from the pancake-vortex model. The different observations in ${\mathrm{DyBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals are in good agreement with a recently given scaling approach.

Nucleation of kinks in 1+1 dimensions.

The nucleation rate of kink-antikink pairs in a sine-Gordon theory at finite temperature is calculated analytically and compared with the results of recent numerical simulations by other authors. The application to the theory of the Bordoni peak is discussed in some detail.

Strain aging and breakaway strain amplitude of damping in NiAl and NiAlZr

Extruded NiAl and NiAlZr alloys often show discontinuous yielding on strain aging in compression at room temperature. Two sets of experiments were conducted to understand the reasons for this yield-point behavior. First, strain-aging experiments were carried out on NiAl alloys containing O to 0.1 at. % Zr. The specimens were all deformed in compression at room temperature at a nominal initial strain rate of 1.1 × 10−4S−1, and the effect of annealing at 700 and 1200 K on the stress-strain curves and the yield strength was studied after an initial prestrain. While annealing at 700 and 1200 K consistently reduced the yield strength of both NiAl and NiAlZr, the effects were quite different. In the case of NiAl, annealing at 1200 K did not result in discontinuous yielding, whereas it generally resulted in a sharp yield point for the Zr containing alloys. Second, the PUCOT (piezoelectric ultrasonic composite oscillator technique) was used to measure the dynamic Young modulus, breakaway strain amplitude, and damping for the alloys. Only small differences were observed in the values of Young's modulus, but the breakaway strain was at least a factor of 2 to 3 lower for NiAl than for NiAlZr. The experimentally determined values of damping were used in the Granato-Lücke model to estimate the binding energy for NiAl. While the binding energy values were found to be in agreement with the calculated values of dislocation kink nucleation and migration energies in this material, to within an order of magnitude, other effects, such as dislocation pinning by quenched-in vacancies, cannot be ruled out. The observations made in this study suggest that the yield-point behavior in NiAl may be due to several factors, such as difficulties in double kink nucleation, and single kink migration, as well as dislocation-vacancy interactions; whereas, the yield-point behavior in the Zr-alloyed material is due at least in part to dislocation-solute interaction.

Kink-antikink dynamics in a realistic heat bath

We study a real-time canonical evolution of field-theoretic systems with boundary coupling to a realistic heat bath. Our method mimicks the infinite extension of a system beyond the boundary. As a first application, we measure kink effective mass and nucleation rate in ϕ 4 field theory in 1+1 dimensions.

Nucleation of a 60° glide dislocation in two-dimensional or three-dimensional growth of epilayers

The nucleation of a 60° glide dislocation in epitaxial thin films is analyzed. Nucleation from either a free surface or from a threading dislocation is considered. In this work, the presence of either infinitely long steps in a two-dimensional film or finite size steps in a two-dimensional or a three-dimensional film is proposed to reduce the activation energy associated with dislocation nucleation. The activation energy is reduced below 40 kT, a value predicted by standard nucleation theory for favorable nucleation, if the step is partially eliminated upon nucleation of a dislocation. However, when the coherency stress is small due to smaller lattice mismatch parameter, the activation energy can not be reduced below 40 kT. In addition, the activation energy is found to be a function of the size of the step but not that of the epilayer. Bowing of a threading dislocation by nucleation of kinks and propagation of the kinks along the dislocation is also analyzed using small angle approximation of the bow out. The activation energy associated with the bow out is again found to be independent of the size of the epilayer thickness. The critical size of the epilayer can be defined if the coherency strain energy remaining in the film is released in the form of thermal energy that helps to overcome the activation energy for nucleation of a dislocation.

Micromechanisms of kinking in rigid-rod polymer fibres

The tensile strengths of fibres of the rigid-rod polymers poly(paraphenylene benzobisthiazole) (PBZT) and poly(paraphenylene benzobisoxazole) (PBZO) are excellent, and therefore are of particular interest for high-performance structural applications. However, these fibres are a factor of ten weaker in compression, with failure occurring by strain localization in welldefined kink bands. Here, we study the morphology of PBZT and PBZO kink bands in detail, in order to help elucidate the molecular mechanisms involved in this deformation process. We found that the typical dimensions of a kink in the direction of the fibre axis (∼ 30 nm) were smaller than the length of an average PBZT or PBZO molecule (100 nm). Also, the boundary between the kinked and unkinked regions was well-defined. Low-dose, high-resolution electron microscopy (HREM) of the kink interior revealed local, high-angle changes in chain orientation, indicative of covalent bond bending or breaking. The kink boundaries exhibit “sharp” or “smooth” features which seem to be related to the local tensile or compressive nature of the stress field. A model for kink nucleation and propagation in terms of partial dislocations is presented and discussed. A stress analysis using this model has been developed, and comparison with experimental data suggests that kinks tend to propagate towards regions of higher compressive stress. This observation is interpreted in terms of dislocation pinning (in areas of hydrostatic tension) and the nucleation of dislocation pairs (in areas of hydrostatic compression) due to the asymmetric nature of the intermolecular energy potential. Finally, practical methods for improving compressive strength based on these mechanistic insights are proposed.

Dislocations around scratches and indents on ±(111) surface of gallium arsenide

The dislocation configurations around microscratches and indents on ±(111) surfaces of GaAs single crystals were studied by X-ray transmission topography, scanning electron microscopy in cathodoluminescence mode and high-voltage transmission electron microscopy. Most of the dislocations generated are loops of screw – B(g) or screw –B(g) – screw character gliding on {111} slip planes parallel or inclined to the surface. The irregular shape of the extended loops gliding parallel to the B surface is due to interaction with other loops and apparent motion involving a double kink nucleation mechanism. The exhibited configuration of dislocation loops suggests a cross-slip orientation of the dissociated screw segments. The direction of propagation of dislocations does not depend on the sense of scratching. Grown-in dislocations are surrounded by a cloud of point defects and they are immobile in contrast to dislocations introduced by indentation.

Thermal stability of Si/GexSi1−x/Si heterostructures

The thermal stability of Si/GexSi1−x/Si (100) heterostructures is studied by in situ electron microscope observations of the thermal relaxation process. Structures are observed to relax by misfit dislocation propagation at both strained interfaces, and are stable to significantly higher temperatures than equivalent strained GexSi1−x layers at a free surface. This observed difference in thermal stability between double and single interface structures is due at least in part to much lower dislocation velocities in the double interface structures, with a measured glide activation energy approximately twice as high as single interface structures. It is argued that this difference in glide activation energies may be due to a smaller kink nucleation activation energy in the single interface structure.

Slip and twinning in high-stress-deformed GaAs and the influence of doping

Abstract The mechanisms of plastic deformation of GaAs at room temperature have been studied using optical microscopy and transmission electron microscopy. This work was performed on crystals deformed by high-stress compression under a confining pressure. Two competitive deformation mechanisms were found: perfect dislocation glide and microtwinning. Twinning is all the more important as the yield stress is high and this stress clearly depends on doping. The microtwins are produced by the gliding of B§ partial dislocations. The mobilities of these partials were also studied; 90° partials are always more mobile than 30° partials. This difference is analysed in terms of nucleation and migration of double kinks on these partial dislocations.

Theory of chemically induced kink formation on cracks in silica. I.3-D crack Green's functions

This article is the first of a pair on a theory of chemically assisted fracture. It includes the Green's function analysis for a three-dimensional crack with a kink on it. Equations are developed for the activation energy for the motion and nucleation of such kinks using information to be found in the second article regarding the force laws appropriate for water attack of silica. The most general conclusion is that lattice trapping barriers to crack motion (including chemical effects) are associated with a narrow core region of the crack, which is in turn connected to the nature of the interatomic force laws of the material (including the modifications of these force laws induced by chemical reactions). Further, it is found that the force law must have a severely “snapping” characteristic in order to assure a narrow core, a feature not to be expected except under certain types of external chemical attack of the crack. Additional results are that the energy to nucleate a kink pair in silica under water attack is in the neighborhood of 2 eV and that the motion energy is of order 0.1 eV. Motion energies are expected to be considerably smaller than formation energies in general.

Temperature, strain rate and fibre orientation effects in the compressive fracture of SiC fibre-reinforced glass-matrix composites

Continuous SiC fibre-reinforced glass-matrix composites have been tested in compression over a wide range of temperatures and loading rates. Both uniaxial and cross-plied fibre orientations were studied. Strength is found to depend sensitively on orientation and loading rate, while temperatures up to 800°C have less effect. Orientation effects are explained in terms of matrix microfracture and fibre buckling. The latter are also shown to control strengthening at very high strain rates, where it is hypothesized that strength is enhanced by inertial effects which inhibit the development of the localized pockets of intense matrix microfracture and general buckling required for the nucleation of fibre kinks.

Kink site saturation mechanism for whisker growth under sputtering conditions

We consider what should happen when surface adsorbed atoms are created at a rate faster than they can be accommodated at kink sites on a surface, such as graphite, for which the nucleation of new growth steps and kinks is difficult. We suppose that this is the condition of common ion beam sputtering systems when the beam current exceeds a critical value. We conclude that, following the nucleation of a second phase as a basal structure, whiskers should grow in the direction of the ion beam, whatever its orientation to the surface normal. Provided that possible attachment sites on the sides of the whiskers are bound, as by termination of dangling bonds by the hydrogen generally present in sputtering systems, the whiskers should grow in length at a constant rate with little or no increase in their diameter. This is because the tips of the whiskers would provide the only nonsaturable source of attachment sites for the surface adsorbed atoms produced by subsequent sputtering. We suggest that this mechanism is responsible for the growth of carbon whiskers with diameters of order 15 nm and remarkably high aspect ratios on graphite surfaces in 1 keV sputtering systems. Such whiskers have been grown to a length in excess of 20 μm and have been demonstrated to be clearly different from the scrolled-graphite structure whiskers obtained by catalytic pyrolysis of hydrocarbons.

Effects of External Shear Stress on the Smallest Double Kink Nucleation Process in Si

A tight-binding type electronic theory (molecular approximation) is used to calculate the formation energy of the double kink E d k for a 1/2[110](1\bar11) (perfect glide set) screw dislocation in covalent semiconductor Si. Effects of external shear stress on the double kink nucleation process are investigated in detail. It is shown that the calculated stress dependence of the E d k is in good agreement with the experimental results of the activation energy for the screw dislocation motion in Si.

A model of creep at intermediate temperatures in aluminium

Abstract A new model of creep at intermediate temperatures in Al is presented, based on a set of previous results of in situ experiments. This model explains the origin of the high forward stresses necessary to extract dislocations from sub-boundaries, and the strong correlation between the speed of sub-boundary migration and the creep rate, asevidenced at different temperatures and by means of in situ strain-rate jumps. High stresses originate from incompatibilities of glide which occur during migration. Under such conditions, it is shown that the creep rate is controlled by a geometrically necessary glide of screw dislocation segments in {100} planes, i.e. by nucleation and propagation of kinks in these non-compact. As the kink energy is estimated from an experimental determination of the ‘dissociation’ energy in Al, all the parameters of the creep law are in good agreement with experimental values.

DISLOCATION MOBILITY MEASUREMENTS : AN ESSENTIAL TOOL FOR UNDERSTANDING THE ATOMIC AND ELECTRONIC CORE STRUCTURES OF DISLOCATIONS I N SEMICONDUCTORS

Thanks to the exploration of a wider range of stress and temperature, and to better instrumental resolution, new phenomena have been investigated and are reviewed here. Deviations to Schmid's law at high stresses and low temperatures, changes in the activation energy at high temperatures, influence on dislocation velocities of dislocation lengths, impurities and point defects and illunlination are reported and discussed in terms of kink nucleation and migration, core structures and reconstruction defects. Some new experiments are also proposed.

Peierls-nabarro plastic deformation in the presence of solute clusters

Solid solution strengthening and weakening in bcc alloys is modeled by a double kink nucleation and lateral motion process in the presence of solute atoms. Classical size or modulus interactions are incorporated into a Peierls-Nabarro dislocation model. The solute atoms are arranged in specified clusters to emphasize the orientation dependence of various superposition effects. A model which fixed the line shape to the pure metal form is shown to be of considerable utility. Nearest and next-nearest neighbor solute-dislocation interactions are responsible for a substantial portion of the changes in the activation energies, but their effects must be reevaluated due to the breakdown of the classical model at such short range. The classical model is not capable of explaining the experimentally observed strengthening, even when nearest and next-nearest neighbor solutes are considered.

The steady state fracture kinetics of crack front spreading

The kinetics study is based on the energetically favourable crack propagation mechanism of double kink nucleation and its subsequent sideways spreading. The analysis was carried out on linearly elastic solids for the case when kink spreading is the rate controlling mechanism. The kink spread distribution is described by a differential equation that is identical with the mass and heat transport equations. The solutions of the differential equation represent the distribution function and the crack propagation velocity as a function of the bond breaking energy ΔG, the work W contributed by the applied stress, and of the temperature. When W≫ΔG/2 the crack velocity increases exponentially with increasing work, decreases steeply with decreasing work, and reduces to zero when W≈ΔG/2. The theory represents well the behavior of ceramic materials and some metals in Region 1 and at the threshold region of stress corrosion cracking. It is of special interest for stress corrosion cracking designs that the threshold stress intensity is independent of the temperature under the conditions of the present investigation.